Vibrational frequency shifts and relaxation rates for a selected vibrational mode in cytochrome C

The vibrational energy relaxation of a selected vibrational mode in cytochrome c--a C-D stretch in the terminal methyl group of Met80--has been studied using equilibrium molecular dynamics simulation and normal mode analysis methods. As demonstrated in the pioneering work of Romesberg and co-workers, isotopic labeling of the C-H (to C-D) stretch in alkyl side chains shifts the stretching frequency to the transparent region of the protein's density of states, making it an effective and versatile probe of protein structure and dynamics. Molecular dynamics trajectories of solvated cytochrome c were run at 300 K, and vibrational population relaxation times were estimated using the classical Landau-Teller-Zwanzig model and a number of semiclassical theories of resonant and two-phonon vibrational relaxation processes. The C-D stretch vibrational population relaxation time is estimated to be T(1) = 14-40 ps; the relatively close agreement between various semiclassical estimates of T(1) lends support to the applicability of those expressions. Normal mode calculations were used to identify the dominant coupling between the protein and C-D oscillator. All bath modes strongly coupled to the C-D stretch are in close proximity. Angle bending modes in the terminal methyl group of Met80 appear to be the most likely acceptor modes defining the mechanism of population relaxation of the C-D vibration.